A colloidal particle, confined in a double well potential, hops
between the two wells at a rate \(r_k\) , named the Kramers' rate,
which is determined by the height \(\delta U\)  of the energy barrier
between the two wells, specifically \(r_k=\tau _0^{-1}\exp ({-{\delta U \over k_BT}})\) , where \(\tau _0\)  is a
characteristic time, \(k_B\)  the Boltzmann constant and \(T\)  the
heat bath temperature [1]}. When the double well
potential \(U\)  is modulated by an external periodic perturbation
whose frequency is close to \(r_k\)  the system presents the
stochastic resonance phenomenon[2]}, i.e. the hops of the
particle between the two wells synchronize with the external
forcing. The stochastic resonance has been widely studied in many
different systems and it has been shown to be a bona fide
resonance looking at the resident time[2]}, [4]},
the Fourier transform of the signal for different noise
intensity[5]}. Numerically, the stochastic resonance has
been characterized by computing the injected work done by the
external agent as a function of noise and frequency
[6]}, [7]}. In a recent experiment [8]} some of us have
studied experimentally the Steady State Fluctuation Theorem (SSFT) in a system composed by a Brownian
particle trapped in a double well potential periodically modulated
by an external driving force. We have measured the energy
injected into the system by the sinusoidal perturbation and we
have analyzed the distributions of work and heat fluctuations. We
find that although the dynamics of the system is strongly
non-linear the SSFT holds for the work integrated on time
intervals which are only a few periods of the driving force. In
this paper we will compare this measured PDF with those derived
analytically from a Langevin dynamics in which the exact potential
of the experiment has been used.
